In many parametric vocoders, such as Sinusoidal Vocoders and Multi-Band Excitation Vocoders, the magnitudes of speech harmonics form an important parameter set from which speech is synthesized. In the case of voiced speech, these are the magnitudes of the pitch frequency harmonics. In the case of unvoiced speech, these are typically the magnitudes of the harmonics of a very low frequency (less than or equal to the lowest pitch frequency). For mixed-voiced speech, these are the magnitudes of the pitch harmonics in the low-frequency band and the harmonics of a very low frequency in the high-frequency band.
Efficient and accurate representation of the harmonic magnitudes is important for ensuring high speech quality in parametric vocoders. Because the pitch frequency changes from person to person and even for the same person depending on the utterance, the number of harmonics required to represent speech is variable. Assuming a speech bandwidth of 3.7 kHz, a sampling frequency of 8 kHz, and a pitch frequency range of 57 Hz to 420 Hz (pitch period range: 19 to 139), the number of speech harmonics can range from 8 to 64. This variable number of harmonic magnitudes makes their representation quite challenging.
A number of techniques have been developed for the efficient representation of the speech harmonic magnitudes. They can be broadly classified into a) Direct quantization, and b) Indirect quantization through a model. In direct quantization, scalar or vector quantization (VQ) techniques are used to quantize the harmonic magnitudes directly. An example is the Non-Square Transform VQ technique described in “Non-Square Transform Vector Quantization for Low-Rate Speech Coding”, P. Lupini and V. Cuperman, Proceedings of the 1995 IEEE Workshop on Speech Coding for Telecommunications, pp. 87–88, September 1995. In this technique, the variable dimension harmonic (log) magnitude vector is transformed into a fixed dimension vector, vector quantized, and transformed back into a variable dimension vector. Another example is the Variable Dimension VQ or VDVQ technique described in “Variable-Dimension Vector Quantization of Speech Spectra for Low-Rate Vocoders”, A. Das, A. Rao, and A. Gersho, Proceedings of the IEEE Data Compression Conference, pp. 420–429, April 1994. In this technique, the VQ codebook consists of high-resolution code vectors with dimension at least equal to the largest dimension of the (log) magnitude vectors to be quantized. For any given dimension, the code vectors are first sub-sampled to the right dimension and then used to quantize the (log) magnitude vector.
In indirect quantization, the harmonic magnitudes are first modeled by another set of parameters, and these model parameters are then quantized. An example of this approach can be found in the IMBE vocoder described in “APCO Project 25 Vocoder Description”, TIA/EIA Interim Standard, July 1993. The (log) magnitudes of the harmonics of a frame of speech are first predicted by the quantized (log) magnitudes corresponding to the previous frame. The (prediction) error magnitudes are next divided into six groups, and each group is transformed by a DCT (Discrete Cosine Transform). The first (or DC) coefficient of each group is combined together and transformed again by another DCT. The coefficients of this second DCT as well as the higher order coefficients of the first six DCTs are then scalar quantized. Depending on the number of harmonic magnitudes, the group size as well as the bits allocated to individual DCT coefficients is changed, keeping the total number of bits constant. Another example can be found in the Sinusoidal Transform Vocoder described in “Low-Rate Speech Coding Based on the Sinusoidal Model”, R. J. McAulay and T. F. Quatieri, Advances in Speech Signal Processing, Eds. S. Furui and M. M. Sondhi, pp. 165–208, Marcel Dekker Inc., 1992. First, an envelope of the harmonic magnitudes is obtained and a (Mel-warped) Cepstrum of this envelope is computed. Next, the cepstral representation is truncated (say, to M values) and transformed back to frequency domain using a Cosine transform. The M frequency domain values (called channel gains) are then quantized using DPCM (Differential Pulse Code Modulation) techniques.
A popular model for representing the speech spectral envelope is the all-pole model, which is typically estimated using linear prediction methods. It is known in the literature that the sampling of the spectral envelope by the pitch frequency harmonics introduces a bias in the model parameter estimation. A number of techniques have been developed to minimize this estimation error. An example of such techniques is Discrete All-Pole Modeling (DAP) as described in “Discrete All-Pole Modeling”, A. El-Jaroudi and J. Makhoul, IEEE Trans. on Signal Processing, Vol. 39, No. 2, pp. 411–423, February 1991. Given a discrete set of spectral samples (or harmonic magnitudes), this technique uses an improved auto-correlation matching condition to come up with the all-pole model parameters through an iterative procedure. Another example is the Envelope Interpolation Linear Predictive (EILP) technique presented in “Spectral Envelope Sampling and Interpolation in Linear Predictive Analysis of Speech”, H. Hermansky, H. Fujisaki, and Y. Sato, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 2.2.1–2.2.4, March 1984. In this technique, the harmonic magnitudes are first interpolated using an averaged parabolic interpolation method. Next, an Inverse Discrete Fourier Transform is used to transform the (interpolated) power spectral envelope to an auto-correlation sequence. The all-pole model parameters viz., predictor coefficients, are then computed using a standard LP method, such as Levinson-Durbin recursion.